基于一致径向基函数的金属塑性成形过程无网格方法分析

径向基函数满足δ条件,可以直接施加本质边界条件.通过耦合多项式基函数可以精确重构任意多项式.将无网格伽辽金方法引入到塑性成形过程模拟,结合刚塑性材料的假设,提出基于一致径向基函数的无网格刚塑性伽辽金方法.采用体积应变率映射法处理体积不可压缩条件;采用反正切摩擦模型在局部坐标系下施加摩擦力边界条件,实现任意边界形状的塑性成形过程模拟.对典型塑性成形过程进行无网格方法分析,并与刚塑性有限元方法及试验数据进行比较,验证了建立方法的可行性.     

金属塑性成形过程无网格伽辽金法数值模拟技术研究

将无网格伽辽金法与刚(粘)塑性流动理论相结合,对无网格伽辽金法在金属塑性成形过程数值模拟中的应用技术进行了研究,分别采用混合变换法和罚函数法实现速度边界条件和体积不变条件,提出了基于刚(粘)塑性力学流动理论的无网格伽辽金法,给出了金属塑性成形无网格伽辽金法数值模拟的关键算法,拓展了无网格方法在金属成形领域的应用范围。典型算例的数值计算结果表明了方法的可行性。     

圆柱体在普通平板间镦粗时应力场的数值模拟

圆柱体在普通平板间镦粗时应力场的数值模拟。基于平衡方程及塑性条件，应用刚塑性力学模型，以实际试件的外形作为边界条件而解决了问题，求出了原高径比Ｈ。／Ｄ０＝２．３３的圆柱体在压下率为１５％～５０％情况下的内部应力场。这与物理模拟定性试验吻会，且进一步证明与完善了刚塑性力学模型的拉应力理论     

圆柱体(H/D>1)在普通平板间镦粗时应力场的定量物理模拟

用光塑性法定量计算了普通平板间镦粗圆柱体 (原始高径比 H0 /D0 =2 )内部应力场 ,其结果与定性物理模拟、数值模拟及刚塑性力学模型的拉应力理论相吻合。同时 ,证明了用光塑性法定量模拟热锻件内部应力场的可行性 ,为解决复杂的 3维问题奠定了基础     

刚(粘)塑性无网格伽辽金方法及其关键技术研究与应用

在国家杰出青年科学基金资助项目《塑性加工工艺及设备》(No.50425517)，以及国家自然科学基金资助项目《金属体积成形过程的刚(粘)塑性无网格伽辽金方法数值模拟理论及其关键技术研究》(No.50575125)支持下，开展刚(粘)塑性无网格伽辽金方法及其关键技术与应用的研究报告，对刚(粘)塑性无网格伽辽金方法的基础理论、数学模型建立方法、关键处理技术在金属塑性成形过程中应用研究的成果。 将无网格伽辽金方法引入塑性成形过程模拟，提出基于刚(粘)塑性理论的无网格伽辽金方法，推导刚度矩阵方程和求解列式。利用变换法施加本质边界条件，采用反正切摩擦模型描述摩擦力边界条件。对于模具边界任意的塑性成形过程，在局部坐标系下施加摩擦力边界条件，给出局部坐标系和整体坐标系的变换矩阵，解决了模具形状任意的二维塑性成形问题摩擦力边界条件的施加问题。采用直接迭代法获得初始速度场，利用Newton Raphson迭代方法求解刚度方程，给出模拟等温塑性成形问题的分析步骤。对于中高温条件下的塑性成形过程，推导出刚(粘)塑性无网格伽辽金方法热力耦合分析模型，给出热力     

圆柱体（H／D〉1）在谱通平板间镦粗时应力场的定量物理模拟

用光塑性法定计算了普通平板间镦粗圆柱体（原始高径比H0/D0=2)内部应力场,其结果与实性物理模拟,数值模拟及刚塑性力学模型的拉应力理论相吻合。同时,证明了用光塑性法定量模拟热锻件内部应力场的可行性,为解决复杂的3维问题奠定了基础。     

用光塑法研究刚塑性力学模型拉应力理论

采用光塑性法定量研究了圆柱体的平板间镦粗。首次把光塑理论与增量理论相结合,用于变形体内应力的定量计算。模拟结果与定性物理模拟相吻合,使圆柱体镦粗的刚塑性力学模型拉应力理论得到了深化。     

采用DEFORM-3D铜扁线拉拔成形的研究

根据刚塑性有限元理论,基于有限元分析软件DEFORM-3D,模拟铜扁线的拉拔成形过程,建立铜扁线拉拔的刚塑性有限元模型,获得相关变形网格、温度场和等效应力等完整信息,得出摩擦因数和模角对拉拔力的影响曲线。     

基于刚塑性流动理论的无网格伽辽金方法

为了对金属体积成形过程进行数值模拟，给出基于刚塑性流动理论的无网格伽辽金方法。由于移动最小二乘近似的非插值特征给无网格伽辽金方法的应用带来了一定的困难，将再生核质点法中的完全变换法与无网格伽辽金方法相结合，通过对速度场的移动最小二乘近似进行修正，实现速度边界条件的精确施加；采用罚函数法引入体积不可压缩条件，运用刚塑性材料的不完全广义变分原理，给出基于刚塑性流动理论的无网格伽辽金方法的离散控制方程以及收敛判据和收敛控制方法。数值计算结果表明方法的可行性及有效性。     

复杂支座挤压成形工艺研究

建立了支座零件成形工艺的刚粘塑性有限元模型，采用三维有限元法对支座成形的两种工艺进行了模拟分析，确定了合理的成形工艺。基于模拟分析的结果，设计出结构合理的成形模具。     

Numerical simulation of three-dimensional bulk forming processes by the element-free Galerkin method

A new approach for simulating three-dimensional (3D) bulk metal forming processes is proposed by combining element-free Galerkin method (EFGM) with the flow theory of 3D rigid-plastic/viscoplastic mechanics. Different from the conventional rigid-plastic FEM, the velocity field is constructed by the moving least-squares (MLS) approximation. Special emphasis is placed on the treatments of essential boundary conditions, incompressibility constraint and friction boundaries. The stiffness equation for the analysis of 3D bulk metal forming using EFGM is derived and its key algorithms are given. To test the validity of the proposed meshless approach, a typical 3D upsetting forming process is analyzed and the numerical results are compared with those obtained by commercialized rigid-plastic FEM software Deform^3D. As results show, when handling 3D plastic deformations, the proposed approach eliminates the need of expensive meshing and remeshing procedures unavoidable in conventional FEM, and still provides results that are in good agreement with finite element predictions.     

杯-杆类零件精密成形过程的有限元分析

以刚塑性有限元分析模型为基础,根据参考文献[1]对金属塑性变形的Mises屈服准则进行修正后,建立了新的数学模型,给出了统一的本构方程,对杯-杆类零件头部精密成形过程进行有限元数值分析.以万向节花键轴为例完成了常温条件下铅试件模拟试验,详细分析了其镦粗、复合挤压和反挤变形过程,计算出了变形体内部的速度场、应力场、应变场的分布结果和成形力随行程(时间)变化曲线,在网格重新划分时采用面积加权平均和体积加权平均相结合的算法,实现新、旧网格体系之间参数的传递,试验结果证明了数值模拟的正确性.     

A simulation of cold-roll forming for elastoplastic materials

A kinematical approach was proposed in a previous paper for predicting the optimal shape and the deformed length of a rigid-plastic metal sheet during cold-roll forming. Because the elastic effects are important in this kind of process, the method has been extended here to elastoplastic materials. In the new formulation, the sheet is still considered as a thin shell and its middle surface is described as a Coons patch depending on one geometrical parameter. Moreover, the material now satisfies a constitutive rate equation in which the corotational rate of stress is used. The Prandtl-Reuss model, including the von Mises yield criterion and the normality flow rule, is used. In order to integrate the elastoplastic constitutive equations, a radial return scheme is adapted so that the plastic power rate is calculated, using a Gauss method. Its minimization gives the optimal shape for a strain hardening elastoplastic material, as well as the optimal velocity field. This approach has been implemented on a workstation and, as for rigid-plastic materials, it gives a very fast simulation of the cold-roll forming process.     

Inclusion of elastic deformation in rigid-plastic finite element analysis

A rigid-plastic finite element method combined with the effect of elastic deformation is proposed. In the present method, elastically and elastic-plastically deforming elements are mixed with rigid-plastically deforming elements in the deforming material. In this formulation based on an implicit scheme, the nodal forces for the rigid-plastic elements are equilibrated with those for the elastic and elastic-plastic elements at the end of each deformation step. The nodal forces for the elastic and elastic-plastic elements are derived by considering the effect of rigid-body rotation during deformation increment. The elastic-plastic element is transformed into the rigid-plastic one during the loading when the elastic strain increment is small. The reverse transformation is carried out in the unloading. This leads to a comparatively small computing time and the improvement of the calculated results. Plane-strain bending of a plate with a round punch is simulated by the present method under a mixed condition of elastic, elastic-plastic and rigid-plastic elements in the plate. Deformation behaviour in early stages of bending is successfully calculated. The calculated amounts of springback are in reasonable agreement with the experimental ones for aluminium plates because the stress distribution in the elastic regions without achieving yielding around the edges of the plate is taken into consideration.     

Upper-bound limit analysis of a rigid-plastic body with frictional interfaces

A finite element formulation of the upper-bound theorem for rigid-plastic solids, generalized to include interfaces with finite friction, is described. As proved by Collins [J. Mech. Phys. Solids 17, 323 (1969)], the usual definition of a kinematically admissible velocity field is unnecessarily restrictive when the upper-bound theorem is applied to many practical problems. This paper shows that a relaxed inequality can be used successfully to derive upper bounds in the presence of Coulomb friction on interfaces, provided one considers a wide enough class of “admissible” velocity fields.One of the major advantages of using a numerical formulation of the upper-bound theorem is that both complex loading geometry and inhomogeneous material behaviour can be easily dealt with. Using a suitable linear approximation of the yield surface, the application of the necessary boundary conditions, the plastic flow rule and the yield criterion lead to a large linear programming problem. The numerical procedure uses constant-strain triangular elements with the unknown velocities as the nodal variables. An additional set of unknowns, the plastic multiplier rates, is associated with each element. Kinematically admissible velocity discontinuities are permitted along specified planes within the finite element mesh. During the solution phase, an active set algorithm is used to solve the linear programming problem.     

Experimental study on optimal plastic rings in the range of large displacements

Circular optimal rings were designed for maximum limit value of load assuming an ideal rigid-plastic material. The paper presents P - δ relations in the range of large displacements obtained in compression and tension tests which were carried out on four types of duraluminum rings with different geometric constraints described by the angle within which the cross section remains constant.

Applicability of rigid-plastic theory to initial optimization of structures exhibiting sensitivity to geometry changes and material hardening is discussed.

The optimal rings without any geometric constraints showed the sensitivity to imperfections and sudden loss of stability with qualitative change of deformation mode. The determination of the best geometric constraints appears as a new optimization criterion when large plastic deformations are present.     

方截面管零件轴压液力成形过程的数值模拟

采用刚塑性有限元对方截面管零件的轴压液力成形过程进行数值模拟,预测其成形结果及可能出现的质量问题,为模具设计及加载路径的优化提供理论依据。     

Collapse modes of a rigid-plastic beam on a rigid-plastic foundation

The carrying capacity of a rigid-plastic Bernoulli beam, resting on a rigid-plastic Winkler foundation, has been analyzed. A detailed study of a particular case, viz. a free-hinged beam loaded by a transverse point force, shows that six collapse modes may appear with 0, 1, 2 and 3 yield hinges. The results are interpreted by means of diagrams, where the various collapse modes appear as area domains.     

曲轴RR法镦锻成形的数值模拟与缺陷预测

针对我国大型曲轴锻造中存在的精度低、加工余量大等问题。采用3维刚塑性有限元法模拟了曲轴RR法镦锻成形过程。通过分析其塑性流动规律与特点,得出模具设计不合理是曲轴拐颊充不满的主要原因,提出了防止该成形缺陷产生的新的模具结构设计方案,从而为曲轴镦锻工艺及模具设计提供了科学依据。